Problem #PRU-61299

Problems Calculus Number sequences Limit of a sequence, convergence Algebra Sequences Recurrent relations Recurrent relations (other)

Problem

The iterative formula of Heron. Prove that the sequence of numbers \(\{x_n\}\) given by the conditions \(x_1 = 1\), \(x_{n + 1} = \frac 12 (x_n + k/x_n)\), converges. Find the limit of this sequence.